#!/usr/bin/env python
# -*- coding:utf-8 -*-
'''
391. Perfect Rectangle

Given N axis-aligned rectangles where N > 0, determine if they all together form an exact cover of a rectangular region.

Each rectangle is represented as a bottom-left point and a top-right point. For example, a unit square is represented as [1,1,2,2]. (coordinate of bottom-left point is (1, 1) and top-right point is (2, 2)).

Example 1:

rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [3,2,4,4],
  [1,3,2,4],
  [2,3,3,4]
]

Return true. All 5 rectangles together form an exact cover of a rectangular region.

Example 2:

rectangles = [
  [1,1,2,3],
  [1,3,2,4],
  [3,1,4,2],
  [3,2,4,4]
]

Return false. Because there is a gap between the two rectangular regions.

Example 3:

rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [1,3,2,4],
  [3,2,4,4]
]

Return false. Because there is a gap in the top center.

Example 4:

rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [1,3,2,4],
  [2,2,4,4]
]

Return false. Because two of the rectangles overlap with each other.

'''
import datetime
import math

class Solution(object):
    def isRectangleCover(self, rectangles):
        """
        :type rectangles: List[List[int]]
        :rtype: bool
        """
        if len(rectangles) == 1:
            return True
        else:
            list_min_2_max_rectangles = []
            min_2_max_rectangle = self.find_bottom_left(rectangles) + self.find_top_right(rectangles)
            list_min_2_max_rectangles += self.split_2_unit(min_2_max_rectangle)

            list_rectangles = []
            for i in rectangles:
                list_rectangles += self.split_2_unit(i)
            
            if len(list_rectangles) == len(list_min_2_max_rectangles):
                if set(list_rectangles) != set(list_min_2_max_rectangles):
                    return False
                else:
                    return True
            else:
                return False

    def find_top_right(self, rectangles):
        max_point_multiple = 0
        max_point = []
        for i in rectangles:
            if i[2] * i[3] > max_point_multiple:
                max_point = [i[2],i[3]]
                max_point_multiple = i[2] * i[3]
        return max_point

    def find_bottom_left(self, rectangles):
        min_point_multiple = None
        min_point = []
        min_point_plus = None
        for i in rectangles:
            if min_point_multiple == None:
                min_point_multiple = i[0] * i[1]
                min_point = [i[0],i[1]]
                min_point_plus = i[0] + i[1]
            if i[0] * i[1] <= min_point_multiple and i[0] + i[1] < min_point_plus:
                min_point_multiple = i[0] * i[1]
                min_point = [i[0],i[1]]
                min_point_plus = i[0] + i[1]
        return min_point

    def split_2_unit(self, rectangle):
        rectangles=[]
        for i in range(rectangle[0], rectangle[2]):
            for j in range(rectangle[1], rectangle[3]):
                new_rectangle=(i,j,i+1,j+1)
                rectangles.append(new_rectangle)
        return rectangles



if __name__=='__main__':
    
    solution=Solution()

    start_time=datetime.datetime.now()
    rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [3,2,4,4],
  [1,3,2,4],
  [2,3,3,4]
]

#Return true. All 5 rectangles together form an exact cover of a rectangular region.
    print(solution.isRectangleCover(rectangles))
#Example 2:

    rectangles = [
  [1,1,2,3],
  [1,3,2,4],
  [3,1,4,2],
  [3,2,4,4]
]

#Return false. Because there is a gap between the two rectangular regions.
    print(solution.isRectangleCover(rectangles))

#Example 3:

    rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [1,3,2,4],
  [3,2,4,4]
]

#Return false. Because there is a gap in the top center.
    print(solution.isRectangleCover(rectangles))

#Example 4:

    rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [1,3,2,4],
  [2,2,4,4]
]
 
    print(solution.isRectangleCover(rectangles))

    rectangles = [[0,0,3,3],[1,1,2,2]]
    print(solution.isRectangleCover(rectangles))

    rectangles = [[0,0,1,1],[0,1,3,2],[1,0,2,2]]
    print(solution.isRectangleCover(rectangles))


    rectangles = [[1,2,4,4],[1,0,4,1],[0,2,1,3],[0,1,3,2],[3,1,4,2],[0,3,1,4],[0,0,1,1]]
    print(solution.isRectangleCover(rectangles))

    rectangles = 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14804,-8111],[8968,14471,9781,14710],[-14992,6634,-14835,7038],[-5208,19112,-5144,19343],[-18795,7825,-18739,8466],[-12160,4263,-12130,4548],[13108,19343,13398,19808],[-18015,529,-17442,640],[3621,803,3832,1118],[19299,-19539,19584,-19515],[-19527,-9406,-19523,-9194],[-12809,-4871,-12748,-4715],[7468,10400,7601,10728],[-1696,-1044,-1609,-654],[8968,2113,9781,2535],[-12748,-6714,-12160,-6569],[-12960,1118,-12951,1258],[-12951,-384,-12809,214],[-19421,-2909,-18795,-2767],[4969,-384,5183,214],[-2015,-3052,-1781,-2909],[-3982,3970,-3933,4164],[-10309,-1090,-10193,-1044],[-10867,10212,-10309,10359],[19584,7061,19992,7199],[-18015,-14704,-17442,-14568],[-9161,4771,-7899,4785],[3621,-2767,3832,-1977],[4819,-15085,4881,-14828],[-12960,10359,-12951,10369],[15689,4164,15884,4263],[-13095,18166,-13057,18439],[-3758,-17630,-3707,-16734],[-4485,-8111,-3982,-7636],[8935,19870,8968,19886],[6403,19870,6728,19886],[19159,-4197,19299,-4004],[3832,20666,4393,20990],[-9573,-14279,-9448,-13457],[18000,-4197,18082,-4004],[19584,-6569,19992,-6552],[-494,-5000,-145,-4715],[12689,16478,13108,16862],[7468,-11595,7601,-11264],[11901,-14568,12654,-14389],[-13417,640,-13095,803],[-9803,12755,-9573,12998],[-7786,-2767,-7538,-1977],[-2802,-3895,-2796,-3649],[-18795,15784,-18739,16423],[11901,-6552,12654,-5468],[13398,5977,13830,6122],[-14470,20150,-13921,20666],[-19523,9733,-19421,10039],[-3758,-5468,-3596,-5462],[-13057,10212,-12960,10359],[-10921,11103,-10867,11137],[-14835,-9406,-14784,-9404],[569,9585,1080,9729],[569,6233,1080,6634],[-4918,15061,-4681,15308],[-14470,-17630,-13921,-16734],[3621,-384,3832,253],[4881,10853,4969,10865],[11901,-5468,12654,-5462],[15348,-19141,15689,-18801],[-5208,19870,-5144,19886],[-18739,-2909,-18486,-2767],[-1609,4164,-1445,4263],[4819,-11730,4881,-11595],[7328,-4197,7468,-4004],[-19523,-7020,-19421,-6714],[14668,-13413,14804,-13365],[12654,-6569,12689,-6552],[-6145,3283,-5354,3858],[3621,-19515,3832,-19431],[3621,-14704,3832,-14568],[-13057,-18539,-12960,-17980],[15884,5977,16099,6122],[-7786,640,-7538,803],[8139,9585,8935,9729],[-7899,-4004,-7786,-3895],[-4681,2113,-4485,2535],[-12960,1384,-12951,1494],[7029,-17630,7081,-16734],[3832,803,4393,1118],[7468,7038,8035,7061],[4393,19870,4819,19886],[14804,-5468,15241,-5462],[300,7721,518,7825],[-5354,6634,-5208,7038],[-10309,7721,-10193,7825],[16517,-3052,17021,-2909],[13108,3262,13398,3283],[-14992,9729,-14835,9733],[-19421,-17630,-18809,-16734],[18000,15013,18082,15061],[-2015,-8111,-1781,-7636],[-2139,-5299,-2015,-5235],[10246,-13413,10303,-13365],[-3883,16862,-3758,17169],[-6145,-19878,-5354,-19709],[12654,-1044,12689,-718],[-12160,-19515,-12130,-19431],[-16900,-19515,-16393,-19431],[15348,11137,15689,11785],[15689,253,15884,529],[-6145,-14704,-5354,-14568],[5757,-6569,6403,-6552],[9781,15061,10246,15308],[-594,-3649,-494,-3101],[11526,-11138,11901,-9654],[11901,15013,12654,15061],[12689,10039,13108,10212],[-14470,4263,-13921,4548],[7081,-18539,7328,-17980],[7328,4263,7468,4548],[-19800,10728,-19623,10853]]
    print(solution.isRectangleCover(rectangles))

    end_time=datetime.datetime.now()
    print(end_time - start_time)

